What was found
AIRCRAFT DEPARTED FROM KAPF ON A REPOSITION LEG AT 1300 ENROUTE TO KTMB. LANDED AND PICKED UP 3 PASSENGERS. DEPARTED KTMB FOR KVNY AT 1430. AFTER TAKEOFF DURING CLIMB OUT, OUTFLOW VALVE FULLY CLOSED AND CABIN PRESSURIZED TO -3500 FT. DIFFERENCE OF PRESSURE EXCEEDED 9.9, AND A DECISION WAS MADE TO DIVERT TO KMIA. EMERGENCY OUTFLOW VALVE WAS OPERATED TO RELIEVE PRESSURE AND AIRCRAFT LANDED WITH NO ISSUES AT -2000 FT. ONCE ON THE GROUND, NORMAL OUTFLOW VALVE WAS MANUALLY DRIVEN OPEN TO EQUALIZE PRESSURE. TROUBLESHOOTING COMMENCED, STILL UNKNOWN WHAT THE ISSUE IS AT THIS POINT. WORKING WITH ENGINEERING TO DETERMINE NEXT PHASE OF ACTION BEFORE RTS.